{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 主成分分析"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#############in MLia chap13 PCA  Prev chap27\n",
    "#P247  \n",
    "#pip install shape\n",
    "#import pca\n",
    "#coding=utf-8\n",
    "import os \n",
    "os.chdir(\"/home/lab466/pythons/pyMLIA35/Ch13PCA\")\n",
    "import matplotlib\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy import *\n",
    "import pca\n",
    "\n",
    "##导入数据 \n",
    "dataMat = pca.loadDataSet('testSet.txt')\n",
    "\n",
    "## 运行PCA\n",
    "lowDMat, reconMat = pca.pca(dataMat, 1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7ff0865aff98>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LcisNQCPSB3Vs5ghG67m1ut2UyhAnzt9kWfNOOijxHkLNlGE4+9AOU+WDAQAX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\nQyJOEASRxZCIEwRBZDH/H/b8rMItg+/mAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff0885fc710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## 显示效果\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.scatter(dataMat[:,0].flatten().A[0], dataMat[:,1].flatten().A[0],marker='^', s=90)\n",
    "ax.scatter(reconMat[:,0].flatten().A[0], reconMat[:,1].flatten().A[0],marker='o', s=50, c='red')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'/home/lab466/pythons/py4fiYves/ipython'"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "os.chdir(\"/home/lab466/pythons/py4fiYves/ipython\")\n",
    "os.getcwd()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "uuid": "a82b3a95-9ee0-4ac3-9601-16972b7728b0"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "#import pandas.io.data as web\n",
    "from pandas_datareader import data, wb\n",
    "from sklearn.decomposition import KernelPCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  主成分分析DAX应用 Principal Component Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#DAX Index and its 30 Stocks\n",
    "symbols = ['ADS.DE', 'ALV.DE', 'BAS.DE', 'BAYN.DE', 'BEI.DE',\n",
    "           'BMW.DE', 'CBK.DE', 'CON.DE', 'DAI.DE', 'DB1.DE',\n",
    "           'DBK.DE', 'DPW.DE', 'DTE.DE',  'FME.DE',\n",
    "           'FRE.DE', 'HEI.DE', 'HEN3.DE', 'IFX.DE', 'LHA.DE',\n",
    "           'LIN.DE', 'LXS.DE', 'MUV2.DE', 'RWE.DE',\n",
    "           'SAP.DE', 'SDF.DE', 'SIE.DE', 'TKA.DE', 'VOW3.DE',\n",
    "           '^GDAXI']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "uuid": "1556b1fa-99da-4122-8aa7-b9e06c069a21"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"\\n%%time\\ndata = pd.DataFrame()\\nfor sym in symbols:\\n    data[sym] = web.DataReader(sym, data_source='yahoo')['Close']\\ndata = data.dropna()\\n\""
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''\n",
    "%%time\n",
    "data = pd.DataFrame()\n",
    "for sym in symbols:\n",
    "    data[sym] = web.DataReader(sym, data_source='yahoo')['Close']\n",
    "data = data.dropna()\n",
    "'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatetimeIndex(['2016-01-01', '2016-01-02', '2016-01-03', '2016-01-04',\n",
       "               '2016-01-05', '2016-01-06', '2016-01-07', '2016-01-08',\n",
       "               '2016-01-09', '2016-01-10',\n",
       "               ...\n",
       "               '2016-09-04', '2016-09-05', '2016-09-06', '2016-09-07',\n",
       "               '2016-09-08', '2016-09-09', '2016-09-10', '2016-09-11',\n",
       "               '2016-09-12', '2016-09-13'],\n",
       "              dtype='datetime64[ns]', length=257, freq='D')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dates = pd.date_range('20160101',periods=257)\n",
    "dates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  186.35,   196.45,    91.05, ...,    22.99,   144.5 , 12953.41],\n",
       "       [  187.4 ,   197.  ,    90.11, ...,    23.5 ,   145.5 , 13013.19],\n",
       "       [  187.  ,   196.2 ,    91.  , ...,    23.5 ,   142.2 , 13003.14],\n",
       "       ...,\n",
       "       [  149.7 ,   141.9 ,    80.52, ...,    21.  ,   125.95, 11166.42],\n",
       "       [  149.65,   142.95,    80.16, ...,    21.46,   125.65, 11165.42],\n",
       "       [  149.4 ,   142.6 ,    79.58, ...,    21.35,   126.  , 11164.42]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cls4 = pd.read_csv('data/4Close.csv',header=None)\n",
    "my_matrix = cls4.as_matrix(columns=None)\n",
    "my_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ADS</th>\n",
       "      <th>ALV</th>\n",
       "      <th>BAS</th>\n",
       "      <th>BAYN</th>\n",
       "      <th>BEI</th>\n",
       "      <th>BMW</th>\n",
       "      <th>CBK</th>\n",
       "      <th>CON</th>\n",
       "      <th>DAI</th>\n",
       "      <th>DB1</th>\n",
       "      <th>...</th>\n",
       "      <th>LIN</th>\n",
       "      <th>LXS</th>\n",
       "      <th>MUV2</th>\n",
       "      <th>RWE</th>\n",
       "      <th>SAP</th>\n",
       "      <th>SDF</th>\n",
       "      <th>SIE</th>\n",
       "      <th>TKA</th>\n",
       "      <th>VOW3</th>\n",
       "      <th>^GDAXI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016-09-09</th>\n",
       "      <td>147.10</td>\n",
       "      <td>141.05</td>\n",
       "      <td>78.95</td>\n",
       "      <td>90.79</td>\n",
       "      <td>79.40</td>\n",
       "      <td>78.32</td>\n",
       "      <td>6.09</td>\n",
       "      <td>172.55</td>\n",
       "      <td>64.12</td>\n",
       "      <td>67.92</td>\n",
       "      <td>...</td>\n",
       "      <td>148.05</td>\n",
       "      <td>57.33</td>\n",
       "      <td>175.30</td>\n",
       "      <td>14.24</td>\n",
       "      <td>78.52</td>\n",
       "      <td>18.24</td>\n",
       "      <td>102.00</td>\n",
       "      <td>20.50</td>\n",
       "      <td>123.65</td>\n",
       "      <td>11168.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-09-10</th>\n",
       "      <td>149.40</td>\n",
       "      <td>142.00</td>\n",
       "      <td>80.30</td>\n",
       "      <td>90.29</td>\n",
       "      <td>80.20</td>\n",
       "      <td>79.37</td>\n",
       "      <td>6.19</td>\n",
       "      <td>174.55</td>\n",
       "      <td>64.91</td>\n",
       "      <td>68.07</td>\n",
       "      <td>...</td>\n",
       "      <td>150.30</td>\n",
       "      <td>58.33</td>\n",
       "      <td>176.60</td>\n",
       "      <td>14.46</td>\n",
       "      <td>80.24</td>\n",
       "      <td>18.43</td>\n",
       "      <td>103.45</td>\n",
       "      <td>21.09</td>\n",
       "      <td>125.20</td>\n",
       "      <td>11167.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-09-11</th>\n",
       "      <td>149.70</td>\n",
       "      <td>141.90</td>\n",
       "      <td>80.52</td>\n",
       "      <td>90.72</td>\n",
       "      <td>80.14</td>\n",
       "      <td>80.17</td>\n",
       "      <td>6.30</td>\n",
       "      <td>175.40</td>\n",
       "      <td>65.34</td>\n",
       "      <td>68.01</td>\n",
       "      <td>...</td>\n",
       "      <td>151.20</td>\n",
       "      <td>57.47</td>\n",
       "      <td>176.45</td>\n",
       "      <td>14.13</td>\n",
       "      <td>80.66</td>\n",
       "      <td>18.64</td>\n",
       "      <td>103.55</td>\n",
       "      <td>21.00</td>\n",
       "      <td>125.95</td>\n",
       "      <td>11166.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-09-12</th>\n",
       "      <td>149.65</td>\n",
       "      <td>142.95</td>\n",
       "      <td>80.16</td>\n",
       "      <td>90.73</td>\n",
       "      <td>80.17</td>\n",
       "      <td>79.92</td>\n",
       "      <td>6.30</td>\n",
       "      <td>174.80</td>\n",
       "      <td>65.45</td>\n",
       "      <td>67.67</td>\n",
       "      <td>...</td>\n",
       "      <td>146.50</td>\n",
       "      <td>57.82</td>\n",
       "      <td>179.15</td>\n",
       "      <td>14.20</td>\n",
       "      <td>80.70</td>\n",
       "      <td>18.62</td>\n",
       "      <td>104.25</td>\n",
       "      <td>21.46</td>\n",
       "      <td>125.65</td>\n",
       "      <td>11165.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-09-13</th>\n",
       "      <td>149.40</td>\n",
       "      <td>142.60</td>\n",
       "      <td>79.58</td>\n",
       "      <td>90.17</td>\n",
       "      <td>80.50</td>\n",
       "      <td>80.07</td>\n",
       "      <td>6.26</td>\n",
       "      <td>173.90</td>\n",
       "      <td>65.22</td>\n",
       "      <td>67.48</td>\n",
       "      <td>...</td>\n",
       "      <td>146.15</td>\n",
       "      <td>57.50</td>\n",
       "      <td>177.95</td>\n",
       "      <td>14.31</td>\n",
       "      <td>80.82</td>\n",
       "      <td>18.60</td>\n",
       "      <td>106.50</td>\n",
       "      <td>21.35</td>\n",
       "      <td>126.00</td>\n",
       "      <td>11164.42</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               ADS     ALV    BAS   BAYN    BEI    BMW   CBK     CON    DAI  \\\n",
       "2016-09-09  147.10  141.05  78.95  90.79  79.40  78.32  6.09  172.55  64.12   \n",
       "2016-09-10  149.40  142.00  80.30  90.29  80.20  79.37  6.19  174.55  64.91   \n",
       "2016-09-11  149.70  141.90  80.52  90.72  80.14  80.17  6.30  175.40  65.34   \n",
       "2016-09-12  149.65  142.95  80.16  90.73  80.17  79.92  6.30  174.80  65.45   \n",
       "2016-09-13  149.40  142.60  79.58  90.17  80.50  80.07  6.26  173.90  65.22   \n",
       "\n",
       "              DB1    ...        LIN    LXS    MUV2    RWE    SAP    SDF  \\\n",
       "2016-09-09  67.92    ...     148.05  57.33  175.30  14.24  78.52  18.24   \n",
       "2016-09-10  68.07    ...     150.30  58.33  176.60  14.46  80.24  18.43   \n",
       "2016-09-11  68.01    ...     151.20  57.47  176.45  14.13  80.66  18.64   \n",
       "2016-09-12  67.67    ...     146.50  57.82  179.15  14.20  80.70  18.62   \n",
       "2016-09-13  67.48    ...     146.15  57.50  177.95  14.31  80.82  18.60   \n",
       "\n",
       "               SIE    TKA    VOW3    ^GDAXI  \n",
       "2016-09-09  102.00  20.50  123.65  11168.42  \n",
       "2016-09-10  103.45  21.09  125.20  11167.42  \n",
       "2016-09-11  103.55  21.00  125.95  11166.42  \n",
       "2016-09-12  104.25  21.46  125.65  11165.42  \n",
       "2016-09-13  106.50  21.35  126.00  11164.42  \n",
       "\n",
       "[5 rows x 29 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.DataFrame(my_matrix,index=dates,columns=['ADS', 'ALV', 'BAS', 'BAYN', 'BEI','BMW', 'CBK', 'CON', 'DAI', 'DB1','DBK', 'DPW', 'DTE', 'FME','FRE', 'HEI', 'HEN3', 'IFX', 'LHA','LIN', 'LXS', 'MUV2', 'RWE','SAP', 'SDF', 'SIE', 'TKA', 'VOW3','^GDAXI'])\n",
    "data.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "DatetimeIndex: 257 entries, 2016-01-01 to 2016-09-13\n",
      "Freq: D\n",
      "Data columns (total 29 columns):\n",
      "ADS       257 non-null float64\n",
      "ALV       257 non-null float64\n",
      "BAS       257 non-null float64\n",
      "BAYN      257 non-null float64\n",
      "BEI       257 non-null float64\n",
      "BMW       257 non-null float64\n",
      "CBK       257 non-null float64\n",
      "CON       257 non-null float64\n",
      "DAI       257 non-null float64\n",
      "DB1       257 non-null float64\n",
      "DBK       257 non-null float64\n",
      "DPW       257 non-null float64\n",
      "DTE       257 non-null float64\n",
      "FME       257 non-null float64\n",
      "FRE       257 non-null float64\n",
      "HEI       257 non-null float64\n",
      "HEN3      257 non-null float64\n",
      "IFX       257 non-null float64\n",
      "LHA       257 non-null float64\n",
      "LIN       257 non-null float64\n",
      "LXS       257 non-null float64\n",
      "MUV2      257 non-null float64\n",
      "RWE       257 non-null float64\n",
      "SAP       257 non-null float64\n",
      "SDF       257 non-null float64\n",
      "SIE       257 non-null float64\n",
      "TKA       257 non-null float64\n",
      "VOW3      257 non-null float64\n",
      "^GDAXI    257 non-null float64\n",
      "dtypes: float64(29)\n",
      "memory usage: 60.2 KB\n"
     ]
    }
   ],
   "source": [
    "data.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ADS</th>\n",
       "      <th>ALV</th>\n",
       "      <th>BAS</th>\n",
       "      <th>BAYN</th>\n",
       "      <th>BEI</th>\n",
       "      <th>BMW</th>\n",
       "      <th>CBK</th>\n",
       "      <th>CON</th>\n",
       "      <th>DAI</th>\n",
       "      <th>DB1</th>\n",
       "      <th>...</th>\n",
       "      <th>LIN</th>\n",
       "      <th>LXS</th>\n",
       "      <th>MUV2</th>\n",
       "      <th>RWE</th>\n",
       "      <th>SAP</th>\n",
       "      <th>SDF</th>\n",
       "      <th>SIE</th>\n",
       "      <th>TKA</th>\n",
       "      <th>VOW3</th>\n",
       "      <th>^GDAXI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016-01-01</th>\n",
       "      <td>186.35</td>\n",
       "      <td>196.45</td>\n",
       "      <td>91.05</td>\n",
       "      <td>114.45</td>\n",
       "      <td>90.96</td>\n",
       "      <td>85.46</td>\n",
       "      <td>12.16</td>\n",
       "      <td>212.95</td>\n",
       "      <td>69.25</td>\n",
       "      <td>90.48</td>\n",
       "      <td>...</td>\n",
       "      <td>182.55</td>\n",
       "      <td>67.29</td>\n",
       "      <td>186.40</td>\n",
       "      <td>20.62</td>\n",
       "      <td>95.49</td>\n",
       "      <td>20.64</td>\n",
       "      <td>115.15</td>\n",
       "      <td>22.99</td>\n",
       "      <td>144.50</td>\n",
       "      <td>12953.41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-02</th>\n",
       "      <td>187.40</td>\n",
       "      <td>197.00</td>\n",
       "      <td>90.11</td>\n",
       "      <td>116.25</td>\n",
       "      <td>91.10</td>\n",
       "      <td>86.42</td>\n",
       "      <td>12.11</td>\n",
       "      <td>214.15</td>\n",
       "      <td>69.40</td>\n",
       "      <td>90.30</td>\n",
       "      <td>...</td>\n",
       "      <td>182.90</td>\n",
       "      <td>67.31</td>\n",
       "      <td>185.95</td>\n",
       "      <td>21.30</td>\n",
       "      <td>95.33</td>\n",
       "      <td>20.73</td>\n",
       "      <td>115.95</td>\n",
       "      <td>23.50</td>\n",
       "      <td>145.50</td>\n",
       "      <td>13013.19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-03</th>\n",
       "      <td>187.00</td>\n",
       "      <td>196.20</td>\n",
       "      <td>91.00</td>\n",
       "      <td>117.25</td>\n",
       "      <td>92.00</td>\n",
       "      <td>86.01</td>\n",
       "      <td>11.43</td>\n",
       "      <td>212.35</td>\n",
       "      <td>68.76</td>\n",
       "      <td>92.21</td>\n",
       "      <td>...</td>\n",
       "      <td>183.05</td>\n",
       "      <td>67.69</td>\n",
       "      <td>186.05</td>\n",
       "      <td>21.41</td>\n",
       "      <td>95.99</td>\n",
       "      <td>20.82</td>\n",
       "      <td>116.50</td>\n",
       "      <td>23.50</td>\n",
       "      <td>142.20</td>\n",
       "      <td>13003.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-04</th>\n",
       "      <td>187.25</td>\n",
       "      <td>197.00</td>\n",
       "      <td>90.45</td>\n",
       "      <td>117.95</td>\n",
       "      <td>92.02</td>\n",
       "      <td>86.30</td>\n",
       "      <td>11.61</td>\n",
       "      <td>213.50</td>\n",
       "      <td>68.36</td>\n",
       "      <td>92.83</td>\n",
       "      <td>...</td>\n",
       "      <td>178.95</td>\n",
       "      <td>68.06</td>\n",
       "      <td>188.35</td>\n",
       "      <td>21.45</td>\n",
       "      <td>95.22</td>\n",
       "      <td>20.94</td>\n",
       "      <td>115.90</td>\n",
       "      <td>23.34</td>\n",
       "      <td>141.55</td>\n",
       "      <td>12991.28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-05</th>\n",
       "      <td>186.85</td>\n",
       "      <td>195.95</td>\n",
       "      <td>90.05</td>\n",
       "      <td>118.70</td>\n",
       "      <td>93.08</td>\n",
       "      <td>87.41</td>\n",
       "      <td>11.68</td>\n",
       "      <td>213.05</td>\n",
       "      <td>68.94</td>\n",
       "      <td>91.05</td>\n",
       "      <td>...</td>\n",
       "      <td>173.35</td>\n",
       "      <td>66.45</td>\n",
       "      <td>186.70</td>\n",
       "      <td>21.37</td>\n",
       "      <td>95.60</td>\n",
       "      <td>20.66</td>\n",
       "      <td>117.40</td>\n",
       "      <td>23.42</td>\n",
       "      <td>143.20</td>\n",
       "      <td>12990.10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               ADS     ALV    BAS    BAYN    BEI    BMW    CBK     CON    DAI  \\\n",
       "2016-01-01  186.35  196.45  91.05  114.45  90.96  85.46  12.16  212.95  69.25   \n",
       "2016-01-02  187.40  197.00  90.11  116.25  91.10  86.42  12.11  214.15  69.40   \n",
       "2016-01-03  187.00  196.20  91.00  117.25  92.00  86.01  11.43  212.35  68.76   \n",
       "2016-01-04  187.25  197.00  90.45  117.95  92.02  86.30  11.61  213.50  68.36   \n",
       "2016-01-05  186.85  195.95  90.05  118.70  93.08  87.41  11.68  213.05  68.94   \n",
       "\n",
       "              DB1    ...        LIN    LXS    MUV2    RWE    SAP    SDF  \\\n",
       "2016-01-01  90.48    ...     182.55  67.29  186.40  20.62  95.49  20.64   \n",
       "2016-01-02  90.30    ...     182.90  67.31  185.95  21.30  95.33  20.73   \n",
       "2016-01-03  92.21    ...     183.05  67.69  186.05  21.41  95.99  20.82   \n",
       "2016-01-04  92.83    ...     178.95  68.06  188.35  21.45  95.22  20.94   \n",
       "2016-01-05  91.05    ...     173.35  66.45  186.70  21.37  95.60  20.66   \n",
       "\n",
       "               SIE    TKA    VOW3    ^GDAXI  \n",
       "2016-01-01  115.15  22.99  144.50  12953.41  \n",
       "2016-01-02  115.95  23.50  145.50  13013.19  \n",
       "2016-01-03  116.50  23.50  142.20  13003.14  \n",
       "2016-01-04  115.90  23.34  141.55  12991.28  \n",
       "2016-01-05  117.40  23.42  143.20  12990.10  \n",
       "\n",
       "[5 rows x 29 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true,
    "uuid": "b4813521-7846-4660-8391-770fea7c318f"
   },
   "outputs": [],
   "source": [
    "dax = pd.DataFrame(data.pop('^GDAXI'))\n",
    "#dax = pd.DataFrame(data.pop('ADS'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "uuid": "03d4a81f-3bd8-47dd-a5b6-84f060fcdf97"
   },
   "outputs": [
    {
     "data": {
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ADS</th>\n",
       "      <th>ALV</th>\n",
       "      <th>BAS</th>\n",
       "      <th>BAYN</th>\n",
       "      <th>BEI</th>\n",
       "      <th>BMW</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016-01-01</th>\n",
       "      <td>186.35</td>\n",
       "      <td>196.45</td>\n",
       "      <td>91.05</td>\n",
       "      <td>114.45</td>\n",
       "      <td>90.96</td>\n",
       "      <td>85.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-02</th>\n",
       "      <td>187.40</td>\n",
       "      <td>197.00</td>\n",
       "      <td>90.11</td>\n",
       "      <td>116.25</td>\n",
       "      <td>91.10</td>\n",
       "      <td>86.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-03</th>\n",
       "      <td>187.00</td>\n",
       "      <td>196.20</td>\n",
       "      <td>91.00</td>\n",
       "      <td>117.25</td>\n",
       "      <td>92.00</td>\n",
       "      <td>86.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-04</th>\n",
       "      <td>187.25</td>\n",
       "      <td>197.00</td>\n",
       "      <td>90.45</td>\n",
       "      <td>117.95</td>\n",
       "      <td>92.02</td>\n",
       "      <td>86.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-05</th>\n",
       "      <td>186.85</td>\n",
       "      <td>195.95</td>\n",
       "      <td>90.05</td>\n",
       "      <td>118.70</td>\n",
       "      <td>93.08</td>\n",
       "      <td>87.41</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               ADS     ALV    BAS    BAYN    BEI    BMW\n",
       "2016-01-01  186.35  196.45  91.05  114.45  90.96  85.46\n",
       "2016-01-02  187.40  197.00  90.11  116.25  91.10  86.42\n",
       "2016-01-03  187.00  196.20  91.00  117.25  92.00  86.01\n",
       "2016-01-04  187.25  197.00  90.45  117.95  92.02  86.30\n",
       "2016-01-05  186.85  195.95  90.05  118.70  93.08  87.41"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[data.columns[:6]].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Applying PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true,
    "uuid": "5ae896a2-8493-4d0c-978c-1b4f26ce2291"
   },
   "outputs": [],
   "source": [
    "scale_function = lambda x: (x - x.mean()) / x.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true,
    "uuid": "4503ea73-aa94-4187-b9c8-cbf00564bf7a"
   },
   "outputs": [],
   "source": [
    "pca = KernelPCA().fit(data.apply(scale_function))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "uuid": "e6f9ebd8-1d61-4047-a254-fe0e524f4c8f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "128"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(pca.lambdas_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "uuid": "1694bb38-778a-403f-82af-0129fdd3a260"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3608., 1717.,  564.,  357.,  248.,  176.,  112.,   75.,   57.,\n",
       "         53.])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.lambdas_[:10].round()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true,
    "uuid": "8c11b92d-c1ea-48dd-a47a-fb4d980b5f40"
   },
   "outputs": [],
   "source": [
    "get_we = lambda x: x / x.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "uuid": "b72fcfcb-d6f0-4101-a59b-c8df516154e8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.50336009, 0.23957398, 0.07871044, 0.04980491, 0.03454329,\n",
       "       0.02449156, 0.01561542, 0.01052413, 0.00801153, 0.00741642])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_we(pca.lambdas_)[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "uuid": "d40695cd-b736-484d-bc11-4755eb1d3448"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9059927071186125"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_we(pca.lambdas_)[:5].sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constructing a PCA Index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true,
    "uuid": "b4691f51-fa25-48d1-855d-907136ee39a7"
   },
   "outputs": [],
   "source": [
    "pca = KernelPCA(n_components=1).fit(data.apply(scale_function))\n",
    "dax['PCA_1'] = pca.transform(-data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "uuid": "9addd109-7de2-4998-b2f0-11c72c3b98da"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7ff07006a668>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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EHa++ClYthzPrwGKG4VfAmbVgyhO9Spv0XaBaxL+CU/Yt71hbAa9PgEUvw7gb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\nFEXxE6qEFUVRFMVP/B8oIKb3yvOpPQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff070057ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "dax.apply(scale_function).plot(figsize=(8, 4))\n",
    "# tag: pca_1\n",
    "# title: German DAX index and PCA index with 1 component"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true,
    "uuid": "4b039aad-93a0-439b-b2d5-d24119604fa4"
   },
   "outputs": [],
   "source": [
    "pca = KernelPCA(n_components=5).fit(data.apply(scale_function))\n",
    "pca_components = pca.transform(-data)\n",
    "weights = get_we(pca.lambdas_)\n",
    "dax['PCA_5'] = np.dot(pca_components, weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "uuid": "fc7a90b6-167b-44dc-9a31-38d479be9026"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7ff06c0dfef0>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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VPaP6ZGI0G5kTPgfU1UQXJgFwLLMMjf4QeudMXvn9FHUGE4n5VRhMytzqodTm0xe/JPxC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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff06c06f278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "dax.apply(scale_function).plot(figsize=(8, 4))\n",
    "# tag: pca_2\n",
    "# title: German DAX index and PCA indices with 1 and 5 components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "uuid": "ceb357ad-d98a-4618-8e73-a6dc77a80436"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([735964., 735965., 735966., 735967., 735968., 735969., 735970.,\n",
       "       735971., 735972., 735973., 735974., 735975., 735976., 735977.,\n",
       "       735978., 735979., 735980., 735981., 735982., 735983., 735984.,\n",
       "       735985., 735986., 735987., 735988., 735989., 735990., 735991.,\n",
       "       735992., 735993., 735994., 735995., 735996., 735997., 735998.,\n",
       "       735999., 736000., 736001., 736002., 736003., 736004., 736005.,\n",
       "       736006., 736007., 736008., 736009., 736010., 736011., 736012.,\n",
       "       736013., 736014., 736015., 736016., 736017., 736018., 736019.,\n",
       "       736020., 736021., 736022., 736023., 736024., 736025., 736026.,\n",
       "       736027., 736028., 736029., 736030., 736031., 736032., 736033.,\n",
       "       736034., 736035., 736036., 736037., 736038., 736039., 736040.,\n",
       "       736041., 736042., 736043., 736044., 736045., 736046., 736047.,\n",
       "       736048., 736049., 736050., 736051., 736052., 736053., 736054.,\n",
       "       736055., 736056., 736057., 736058., 736059., 736060., 736061.,\n",
       "       736062., 736063., 736064., 736065., 736066., 736067., 736068.,\n",
       "       736069., 736070., 736071., 736072., 736073., 736074., 736075.,\n",
       "       736076., 736077., 736078., 736079., 736080., 736081., 736082.,\n",
       "       736083., 736084., 736085., 736086., 736087., 736088., 736089.,\n",
       "       736090., 736091., 736092., 736093., 736094., 736095., 736096.,\n",
       "       736097., 736098., 736099., 736100., 736101., 736102., 736103.,\n",
       "       736104., 736105., 736106., 736107., 736108., 736109., 736110.,\n",
       "       736111., 736112., 736113., 736114., 736115., 736116., 736117.,\n",
       "       736118., 736119., 736120., 736121., 736122., 736123., 736124.,\n",
       "       736125., 736126., 736127., 736128., 736129., 736130., 736131.,\n",
       "       736132., 736133., 736134., 736135., 736136., 736137., 736138.,\n",
       "       736139., 736140., 736141., 736142., 736143., 736144., 736145.,\n",
       "       736146., 736147., 736148., 736149., 736150., 736151., 736152.,\n",
       "       736153., 736154., 736155., 736156., 736157., 736158., 736159.,\n",
       "       736160., 736161., 736162., 736163., 736164., 736165., 736166.,\n",
       "       736167., 736168., 736169., 736170., 736171., 736172., 736173.,\n",
       "       736174., 736175., 736176., 736177., 736178., 736179., 736180.,\n",
       "       736181., 736182., 736183., 736184., 736185., 736186., 736187.,\n",
       "       736188., 736189., 736190., 736191., 736192., 736193., 736194.,\n",
       "       736195., 736196., 736197., 736198., 736199., 736200., 736201.,\n",
       "       736202., 736203., 736204., 736205., 736206., 736207., 736208.,\n",
       "       736209., 736210., 736211., 736212., 736213., 736214., 736215.,\n",
       "       736216., 736217., 736218., 736219., 736220.])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib as mpl\n",
    "mpl_dates = mpl.dates.date2num(data.index.to_pydatetime())\n",
    "mpl_dates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "uuid": "60ae390c-9534-4e57-bc1e-42e261d0abc9"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7ff05c5482b0>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GDBDhk1DqHwbzN5VQHqrd1mKpViBiMto6Eg3qSqkWEYnYTJkyl4ce/og3J31H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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff05c68ba58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 4))\n",
    "plt.scatter(dax['PCA_5'], dax['^GDAXI'], c=mpl_dates)\n",
    "lin_reg = np.polyval(np.polyfit(dax['PCA_5'],\n",
    "                                dax['^GDAXI'], 1),\n",
    "                                dax['PCA_5'])\n",
    "plt.plot(dax['PCA_5'], lin_reg, 'r', lw=3)\n",
    "plt.grid(True)\n",
    "plt.xlabel('PCA_5')\n",
    "plt.ylabel('^GDAXI')\n",
    "plt.colorbar(ticks=mpl.dates.DayLocator(interval=250),\n",
    "                format=mpl.dates.DateFormatter('%d %b %y'))\n",
    "# tag: pca_3\n",
    "# title: DAX return values against PCA return values with linear regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true,
    "uuid": "2c9bea6f-bed0-49d0-83ad-a30c17b31922"
   },
   "outputs": [],
   "source": [
    "#cut_date = '2011/7/1'\n",
    "cut_date = '2016/7/1'\n",
    "early_pca = dax[dax.index < cut_date]['PCA_5']\n",
    "early_reg = np.polyval(np.polyfit(early_pca,\n",
    "                dax['^GDAXI'][dax.index < cut_date], 1),\n",
    "                early_pca)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true,
    "uuid": "0df5fdce-32ae-4b85-836d-91355f33bb90"
   },
   "outputs": [],
   "source": [
    "late_pca = dax[dax.index >= cut_date]['PCA_5']\n",
    "late_reg = np.polyval(np.polyfit(late_pca,\n",
    "                dax['^GDAXI'][dax.index >= cut_date], 1),\n",
    "                late_pca)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "uuid": "ad8b2336-b13f-49a2-92b9-3f7b340be327"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7ff05c3f67f0>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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kI/DUahofP/t77vpoMna1CGzC4InAcZtX8uRb/xf32r2uewQWbKpKMPCbX/Tl9JNPAOBP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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff06c0c5128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 4))\n",
    "plt.scatter(dax['PCA_5'], dax['^GDAXI'], c=mpl_dates)\n",
    "plt.plot(early_pca, early_reg, 'r', lw=3)\n",
    "plt.plot(late_pca, late_reg, 'r', lw=3)\n",
    "plt.grid(True)\n",
    "plt.xlabel('PCA_5')\n",
    "plt.ylabel('^GDAXI')\n",
    "plt.colorbar(ticks=mpl.dates.DayLocator(interval=250),\n",
    "                format=mpl.dates.DateFormatter('%d %b %y'))\n",
    "# tag: pca_7\n",
    "# title: DAX index values against PCA index values with early and late regression (regime switch)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pearson和Spearman相关系数例子"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from math import sqrt \n",
    "def multipl(a,b):\n",
    "    sumofab=0.0\n",
    "    for i in range(len(a)):\n",
    "        temp=a[i]*b[i]\n",
    "        sumofab+=temp\n",
    "    return sumofab \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def corrcoef(x,y):\n",
    "    n=len(x)\n",
    "    #求和\n",
    "    sum1=sum(x)\n",
    "    sum2=sum(y)\n",
    "    #求乘积之和\n",
    "    sumofxy=multipl(x,y)\n",
    "    #求平方和\n",
    "    sumofx2 = sum([pow(i,2) for i in x])\n",
    "    sumofy2 = sum([pow(j,2) for j in y])\n",
    "    num=sumofxy-(float(sum1)*float(sum2)/n)\n",
    "    #计算皮尔逊相关系数\n",
    "    den=sqrt((sumofx2-float(sum1**2)/n)*(sumofy2-float(sum2**2)/n))\n",
    "    return num/den\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.47140452079103173\n"
     ]
    }
   ],
   "source": [
    "x = [0,1,0,3]\n",
    "y = [0,1,1,1]\n",
    " \n",
    "print (corrcoef(x,y)) #0.471404520791\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SpearmanrResult(correlation=0.0, pvalue=1.0)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Spearman's correlation coefficient\n",
    "\n",
    "from scipy.stats import spearmanr\n",
    "spearmanr([0.3, 0.2, 0.2], [0.5, 0.6, 0.4])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SpearmanrResult(correlation=1.0, pvalue=0.0)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spearmanr([0.1, 0.2, 0.3], [0.1, 0.2, 0.3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
